A bicycle wheel consists of a diameter of 64.6 cm and a mass of 1.82 kg. Suppose that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is positioned on a stationary stand and a resistive force of 123 N is applied tangent to the rim of the tire.
(i) Determine the force which should be exerted by a chain passing over an 8.94 cm diameter sprocket when the wheel is to attain an acceleration of 4.45 rad/s2?
(ii) What force is needed when the chain shifts to a 5.65 cm diameter sprocket?